The purpose of this paper is to provide a general technique for defining and analyzing smoothing operators for use in multigrid algorithms. The smoothing operators considered are based on subspace decomposition and include point, line, and block versions of Jacobi and Gauss-Seidel iteration as well as generalizations. We shall show that these smoothers will be effective in multigrid algorithms ...

We study the spectral radius algebras associated to compact operators and we give some sufficient conditions for membership in them. Since it is known that each such algebra has an invariant subspace this leads to some new invariant subspace theorems. We will also compare our method with several well known approaches to the invariant subspace problem. MSC (2000): Primary 47A65; Secondary 47A62,...

This paper deals with local spectral properties of Extended Hamilton operators and their adjoint operators. The relationship between the (strongly decomposability, hyperinvariant subspace problem, etc.) corresponding is obtained.

In the setting of operators on Hilbert spaces, we prove that every quasinilpotent operator has a non-trivial closed invariant subspace if and only pair idempotents with commutator common subspace. We also present geometric characterization subspaces classify are essentially idempotent.